
Although the objective function of (P1-\(j\) -\(n_j\) ) is concave w.r.t. \(\vartheta _{j,n_j}\) , it is still non-convex due to the unit-modulus constraint in (REF ). To address this issue, we relax it as \(|\vartheta _{j,n_j}|\le 1\)  and denote the relaxed problem as (P2-\(j\) -\(n_j\) ), which is convex and thus can be solved by standard convex optimization methods, such as the interior point method [1]}. Denote \(\vartheta _{j,n_j}^{\star }\)  as the optimal solution for (P2-\(j\) -\(n_j\) ), which may not be feasible to (P1-\(j\) -\(n_j\) ) due to the unit-modulus constraint in (REF ). As such, the obtained solution should be projected to the feasible region of (P1-\(j\) -\(n_j\) ) as follows [2]}
\(\vartheta ^{\star \star }_{j,n_j}=\vartheta _{j,n_j}^{\star }/|\vartheta _{j,n_j}^{\star }|.\) 
